Finite Group Databasebeta

← C2×#10590267 #11865701

Subgroups — C2×#10590267 #11865701

Order 1152.

1069 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#875C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C22×#3718C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic
5C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic
8#10590267C218yesmaximal, direct product factor
9C2×#5054—31nomaximal
10C2×#5028—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×C4×Dic3—21no—
22C3×#875—22no—
23C3×#875C2214yes—
24C3×C4×Dic6—22no—
25C3×C4×Dic6C2214yescomplemented
26C2×#3718—24no—
27C2×#3718C2214yescomplemented
28C2×#3715—24no—
29C2×#3715C2214yes—
30C4⋊(C3⋊(C3⋊C8))C2214yescomplemented
31#63565C2214yescomplemented
32#63562C2214yes—
33C2×C3×#124—31no—
34C2×C3×C4×Q8—31no—
35C22×#216—31no—
36C22×#216—31no—
37C22×#215—31no—
38C22×#214—31no—
39C2×#875D311yescharacteristic
40C2×C4×Dic6D311yescharacteristic, complemented
41C2×#835—31no—
42C2×#832—31no—
43#5054—38no—
44#5028—38no—
45C2×#810—31no—
46C2×#809—31no—
47C2×C4⋊(C3⋊C8)—31no—
48C2×C4⋊(C3⋊C8)—31no—
49C2×C4⋊(C3⋊C8)—61no—
50C23×C3×D3—21no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—21no—
60C2×C3×D12C2312yes—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D414yes—
67C2×C3×Dic6C2312yes—
68C2×C3×Dic6C2312yes—
69C32×C42D412yes—
70C32×C42C2312yes—
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)—22no—
73C2×C3⋊(C3⋊C8)C2312yes—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×(C2×D3)⋊C4—24no—
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—24no—
80C3×C4×Dic3—24no—
81#3718—28no—
82#3715—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C22×Dic6C2×D311yescharacteristic
90C3×#124—34no—
91C3×#124—62no—
92C3×C4×Q8—34no—
93C3×C4×Q8—62no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—61no—
96C2×C3×C22⋊C4—61no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C42—21no—
99C2×C3×C42—61no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C2×D311yescharacteristic
102C2×#216—34no—
103C2×#216—34no—
104C2×#216—64no—
105C2×#216—64no—
106C2×#215—34no—
107C2×#215—64no—
108C2×#214—34no—
109C2×#214—64no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×Dic3⋊C4—21no—
114C2×C4×Dic3—21no—
115C22×C3⋊C8—31no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—61no—
120C22×C3⋊C8—61no—
121#875—22no—
122#875C2×D314yes—
123C4×Dic6—22no—
124C4×Dic6C2×D314yescomplemented
125#835—34no—
126#832—34no—
127#810—34no—
128#809—34no—
129C4⋊(C3⋊C8)—34no—
130C4⋊(C3⋊C8)—34no—
131C4⋊(C3⋊C8)—64no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—42no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D412yes—
141C2×C32×C4C2×D412yes—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4112yes—
144C2×C32×C4C2411yescharacteristic
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—42no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—42no—
154C3×Dic6—24no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—42no—
159C3×Dic6C2×D414yes—
160C3⋊(C3⋊C8)—22no—
161C3⋊(C3⋊C8)—22no—
162C22×Q16—91no—
163C22×SD16—91no—
164C2×#124—31no—
165C2×C4×Q8—31no—
166#464—98no—
167C2×C4⋊C8—91no—
168C2×#103—91no—
169C2×#102—91no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×Q8—34no—
173C2×C3×Q8—32no—
174C2×C3×Q8—32no—
175C2×C3×Q8—62no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—62no—
179C2×C3×Q8—62no—
180C2×C3×D4—32no—
181C2×C3×D4—62no—
182C2×C3×D4—62no—
183C2×C3×D4—61no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C22×C3×C4#6711yescharacteristic
191C22×C3×C4#6711yescharacteristic
192C22×C3×C4#6711yescharacteristic
193C22×C3×C4#6711yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C2×D12—22no—
200C2×D12—22no—
201C2×D12—21no—
202C2×D12C22×D312yes—
203C2×Dic6—22no—
204C2×Dic6—21no—
205C2×Dic6—22no—
206C2×Dic6—22no—
207C2×Dic6—21no—
208C2×Dic6D1214yes—
209C2×Dic6C22×D312yes—
210C2×Dic6C22×D312yes—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—64no—
213C3×C4⋊C4—61no—
214C3×C22⋊C4—64no—
215C3×C22⋊C4—64no—
216C3×C42—22no—
217C3×C42—22no—
218C3×C42—64no—
219C3×C42#6712yes—
220C3×C42#6712yes—
221C3×C42C22×D312yes—
222C3×C42C22×D312yes—
223#216—68no—
224#216—68no—
225#215—68no—
226#214—68no—
227(C2×D3)⋊C4—24no—
228(C2×D3)⋊C4—24no—
229C4⋊Dic3—21no—
230C4⋊Dic3C22×D312yes—
231Dic3⋊C4—24no—
232C4×Dic3—24no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8—62no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—62no—
243C2×C3⋊C8—122no—
244C2×C3⋊C8—122no—
245C22×C32#12112yes—
246C22×C32#13512yes—
247C22×C32#13712yes—
248C22×C32C22×D411yescharacteristic
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—84no—
253C32×C4—22no—
254C32×C4—22no—
255C32×C4#12112yes—
256C32×C4C22×D411yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3×Dic3—24no—
259C3×Dic3—42no—
260C3×Dic3—42no—
261C22×Q8—31no—
262C22×Q8—31no—
263C22×D4—31no—
264C2×Q16—94no—
265C2×Q16—184no—
266C2×SD16—94no—
267C2×SD16—184no—
268C22×C8—91no—
269C22×C8—91no—
270#124—34no—
271#124—62no—
272C4×Q8—34no—
273C4×Q8—62no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—61no—
276C2×C22⋊C4—61no—
277C2×C22⋊C4—61no—
278C2×C42—61no—
279C2×C42D3211yescharacteristic
280C4⋊C8—94no—
281#103—94no—
282#102—94no—
283C23×C3—21no—
284C23×C3—62no—
285C23×C3—122no—
286C23×C3—122no—
287C23×C3—122no—
288C23×C3C2×#6711yescharacteristic
289C23×C3C2×#6711yescharacteristic
290C22×D3—22no—
291C22×D3—42no—
292C22×D3—42no—
293C22×D3—42no—
294C3×Q8—34no—
295C3×Q8—64no—
296C3×Q8—62no—
297C3×Q8—62no—
298C3×Q8—62no—
299C3×Q8—122no—
300C3×D4—62no—
301C3×D4—62no—
302C3×D4—122no—
303C2×C3×C4—24no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—22no—
314C2×C3×C4—42no—
315C2×C3×C4—64no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—122no—
320C2×C3×C4—122no—
321C2×C3×C4C2×D1212yes—
322C2×C3×C4#23512yes—
323C2×C3×C4D3×D412yes—
324C2×C3×C4#23712yes—
325C2×C3×C4C2×#6712yes—
326C2×C3×C4C2×#6712yes—
327C2×C3×C4C2×#6712yes—
328C2×C3×C4C2×#6712yes—
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×Dic3—24no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—42no—
338C2×Dic3—42no—
339D12—22no—
340D12—22no—
341D12—42no—
342Dic6—24no—
343Dic6—22no—
344Dic6—22no—
345Dic6—22no—
346Dic6—42no—
347Dic6C2×D1214yes—
348C3⋊C8—62no—
349C3⋊C8—62no—
350C3⋊C8—62no—
351C3⋊C8—62no—
352C3⋊C8—122no—
353C3⋊C8—122no—
354C2×C32#46414yescomplemented
355C2×C32C2×#12111yescharacteristic
356C2×C32C2×#13511yescharacteristic
357C2×C32C2×#13711yescharacteristic
358C3×D3—82no—
359C24—61no—
360C2×Q8—32no—
361C2×Q8—32no—
362C2×Q8—34no—
363C2×Q8—62no—
364C2×Q8—61no—
365C2×Q8—61no—
366C2×Q8—62no—
367C2×Q8—62no—
368C2×D4—32no—
369C2×D4—62no—
370C2×D4—62no—
371C2×D4—61no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4#62511yescharacteristic
376C22×C4#62511yescharacteristic
377C22×C4C2×D3211yescharacteristic
378Q16—188no—
379SD16—188no—
380C2×C8—92no—
381C2×C8—92no—
382C2×C8—182no—
383C2×C8—182no—
384C4⋊C4—32no—
385C4⋊C4—61no—
386C4⋊C4—64no—
387C22⋊C4—64no—
388C22⋊C4—64no—
389C42—64no—
390C42#62512yes—
391C42C2×D3212yes—
392C22×C3—21no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—122no—
397C22×C3—122no—
398C22×C3—122no—
399C22×C3—244no—
400C22×C3#93012yes—
401C22×C3#93812yes—
402C22×C3#94212yes—
403C22×C3#95012yes—
404C22×C3#95012yes—
405C22×C3#95112yes—
406C22×C3C22×#6711yescharacteristic
407C22×C3C22×#6711yescharacteristic
408C2×D3—42no—
409C2×D3—42no—
410C2×D3—42no—
411C2×D3—84no—
412C3×C4—24no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—22no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—22no—
420C3×C4—42no—
421C3×C4—64no—
422C3×C4—122no—
423C3×C4—122no—
424C3×C4#93012yes—
425C3×C4#93812yes—
426C3×C4C22×D1211yescharacteristic
427C3×C4C2×#23511yescharacteristic
428C3×C4C2×D3×D411yescharacteristic
429C3×C4C2×#23711yescharacteristic
430Dic3—24no—
431Dic3—42no—
432Dic3—42no—
433C32C2×#46411yescharacteristic, complemented, Sylow
434C23—62no—
435C23—122no—
436C23—122no—
437C23—122no—
438C23C2×#62511yescharacteristic
439Q8—34no—
440Q8—62no—
441Q8—64no—
442Q8—62no—
443Q8—62no—
444Q8—122no—
445D4—62no—
446D4—62no—
447D4—122no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—62no—
451C2×C4—64no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—122no—
455C2×C4—122no—
456C2×C4#379512yes—
457C2×C4D3×D1212yes—
458C2×C4C2×#62512yes—
459C2×C4C2×#62512yes—
460C2×C4C2×#62511yescharacteristic
461C2×C4C22×D3211yescharacteristic
462C8—182no—
463C8—182no—
464C2×C3—24no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—242no—
469C2×C3#502814yescomplemented
470C2×C3#505414yescomplemented
471C2×C3C2×#93011yescharacteristic
472C2×C3C2×#93811yescharacteristic
473C2×C3C2×#94211yescharacteristic
474C2×C3C2×#95011yescharacteristic
475C2×C3C2×#95011yescharacteristic
476C2×C3C2×#95111yescharacteristic
477D3—82no—
478C22—122no—
479C22—122no—
480C22—122no—
481C22—244no—
482C22#6382212yes—
483C22#6382712yes—
484C22#6390812yes—
485C22C22×#62511yescharacteristic
486C4—22no—
487C4—22no—
488C4—64no—
489C4—122no—
490C4—122no—
491C4#6390812yes—
492C4C2×#379511yescharacteristic
493C4C2×D3×D1211yescharacteristic
494C3—21no—
495C3C2×#502811yescharacteristic, complemented
496C3C2×#505411yescharacteristic, complemented
497C2—242no—
498C2#1059026714yesdirect product factor
499C2C2×#6382211yescharacteristic
500C2C2×#6382711yescharacteristic
501C2C2×#6390811yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C22×#3718C2semidirect
5. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
6. C2×#63565C2semidirect
8. #10590267C2direct (N × H)
25. C3×C4×Dic6C22semidirect
27. C2×#3718C22semidirect
30. C4⋊(C3⋊(C3⋊C8))C22semidirect
31. #63565C22semidirect
40. C2×C4×Dic6D3semidirect
124. C4×Dic6C2×D3semidirect
354. C2×C32#464semidirect
433. C32C2×#464semidirect
469. C2×C3#5028semidirect
470. C2×C3#5054semidirect
495. C3C2×#5028semidirect
496. C3C2×#5054semidirect
498. C2#10590267direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#8752
C2×C3×C4×Dic62
C22×#37182
C22×#37152
C2×C4⋊(C3⋊(C3⋊C8))2
C2×#635652
C2×#635622
#105902672
C2×#50543
C2×#50283